Ejemplo n.º 1
0
        /**
         * return a sqrt root - the routine verifies that the calculation returns the right value - if
         * none exists it returns null.
         */
        public override ECFieldElement Sqrt()
        {
            /*
             * Raise this element to the exponent 2^254 - 2^30 - 2^7 - 2^6 - 2^5 - 2^4 - 2^2
             *
             * Breaking up the exponent's binary representation into "repunits", we get:
             * { 223 1s } { 1 0s } { 22 1s } { 4 0s } { 2 1s } { 2 0s}
             *
             * Therefore we need an addition chain containing 2, 22, 223 (the lengths of the repunits)
             * We use: 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
             */

            uint[] x1 = this.x;
            if (Nat256.IsZero(x1) || Nat256.IsOne(x1))
            {
                return(this);
            }

            uint[] x2 = Nat256.Create();
            SecP256K1Field.Square(x1, x2);
            SecP256K1Field.Multiply(x2, x1, x2);
            uint[] x3 = Nat256.Create();
            SecP256K1Field.Square(x2, x3);
            SecP256K1Field.Multiply(x3, x1, x3);
            uint[] x6 = Nat256.Create();
            SecP256K1Field.SquareN(x3, 3, x6);
            SecP256K1Field.Multiply(x6, x3, x6);
            uint[] x9 = x6;
            SecP256K1Field.SquareN(x6, 3, x9);
            SecP256K1Field.Multiply(x9, x3, x9);
            uint[] x11 = x9;
            SecP256K1Field.SquareN(x9, 2, x11);
            SecP256K1Field.Multiply(x11, x2, x11);
            uint[] x22 = Nat256.Create();
            SecP256K1Field.SquareN(x11, 11, x22);
            SecP256K1Field.Multiply(x22, x11, x22);
            uint[] x44 = x11;
            SecP256K1Field.SquareN(x22, 22, x44);
            SecP256K1Field.Multiply(x44, x22, x44);
            uint[] x88 = Nat256.Create();
            SecP256K1Field.SquareN(x44, 44, x88);
            SecP256K1Field.Multiply(x88, x44, x88);
            uint[] x176 = Nat256.Create();
            SecP256K1Field.SquareN(x88, 88, x176);
            SecP256K1Field.Multiply(x176, x88, x176);
            uint[] x220 = x88;
            SecP256K1Field.SquareN(x176, 44, x220);
            SecP256K1Field.Multiply(x220, x44, x220);
            uint[] x223 = x44;
            SecP256K1Field.SquareN(x220, 3, x223);
            SecP256K1Field.Multiply(x223, x3, x223);

            uint[] t1 = x223;
            SecP256K1Field.SquareN(t1, 23, t1);
            SecP256K1Field.Multiply(t1, x22, t1);
            SecP256K1Field.SquareN(t1, 6, t1);
            SecP256K1Field.Multiply(t1, x2, t1);
            SecP256K1Field.SquareN(t1, 2, t1);

            uint[] t2 = x2;
            SecP256K1Field.Square(t1, t2);

            return(Nat256.Eq(x1, t2) ? new SecP256K1FieldElement(t1) : null);
        }
Ejemplo n.º 2
0
        public override ECPoint Add(ECPoint b)
        {
            if (this.IsInfinity)
            {
                return(b);
            }
            if (b.IsInfinity)
            {
                return(this);
            }
            if (this == b)
            {
                return(Twice());
            }

            ECCurve curve = this.Curve;

            SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.RawXCoord, Y1 = (SecP256K1FieldElement)this.RawYCoord;
            SecP256K1FieldElement X2 = (SecP256K1FieldElement)b.RawXCoord, Y2 = (SecP256K1FieldElement)b.RawYCoord;

            SecP256K1FieldElement Z1 = (SecP256K1FieldElement)this.RawZCoords[0];
            SecP256K1FieldElement Z2 = (SecP256K1FieldElement)b.RawZCoords[0];

            uint c;

            uint[] tt1 = Nat256.CreateExt();
            uint[] t2  = Nat256.Create();
            uint[] t3  = Nat256.Create();
            uint[] t4  = Nat256.Create();

            bool Z1IsOne = Z1.IsOne;

            uint[] U2, S2;
            if (Z1IsOne)
            {
                U2 = X2.x;
                S2 = Y2.x;
            }
            else
            {
                S2 = t3;
                SecP256K1Field.Square(Z1.x, S2);

                U2 = t2;
                SecP256K1Field.Multiply(S2, X2.x, U2);

                SecP256K1Field.Multiply(S2, Z1.x, S2);
                SecP256K1Field.Multiply(S2, Y2.x, S2);
            }

            bool Z2IsOne = Z2.IsOne;

            uint[] U1, S1;
            if (Z2IsOne)
            {
                U1 = X1.x;
                S1 = Y1.x;
            }
            else
            {
                S1 = t4;
                SecP256K1Field.Square(Z2.x, S1);

                U1 = tt1;
                SecP256K1Field.Multiply(S1, X1.x, U1);

                SecP256K1Field.Multiply(S1, Z2.x, S1);
                SecP256K1Field.Multiply(S1, Y1.x, S1);
            }

            uint[] H = Nat256.Create();
            SecP256K1Field.Subtract(U1, U2, H);

            uint[] R = t2;
            SecP256K1Field.Subtract(S1, S2, R);

            // Check if b == this or b == -this
            if (Nat256.IsZero(H))
            {
                if (Nat256.IsZero(R))
                {
                    // this == b, i.e. this must be doubled
                    return(this.Twice());
                }

                // this == -b, i.e. the result is the point at infinity
                return(curve.Infinity);
            }

            uint[] HSquared = t3;
            SecP256K1Field.Square(H, HSquared);

            uint[] G = Nat256.Create();
            SecP256K1Field.Multiply(HSquared, H, G);

            uint[] V = t3;
            SecP256K1Field.Multiply(HSquared, U1, V);

            SecP256K1Field.Negate(G, G);
            Nat256.Mul(S1, G, tt1);

            c = Nat256.AddBothTo(V, V, G);
            SecP256K1Field.Reduce32(c, G);

            SecP256K1FieldElement X3 = new SecP256K1FieldElement(t4);

            SecP256K1Field.Square(R, X3.x);
            SecP256K1Field.Subtract(X3.x, G, X3.x);

            SecP256K1FieldElement Y3 = new SecP256K1FieldElement(G);

            SecP256K1Field.Subtract(V, X3.x, Y3.x);
            SecP256K1Field.MultiplyAddToExt(Y3.x, R, tt1);
            SecP256K1Field.Reduce(tt1, Y3.x);

            SecP256K1FieldElement Z3 = new SecP256K1FieldElement(H);

            if (!Z1IsOne)
            {
                SecP256K1Field.Multiply(Z3.x, Z1.x, Z3.x);
            }
            if (!Z2IsOne)
            {
                SecP256K1Field.Multiply(Z3.x, Z2.x, Z3.x);
            }

            ECFieldElement[] zs = new ECFieldElement[] { Z3 };

            return(new SecP256K1Point(curve, X3, Y3, zs, IsCompressed));
        }
Ejemplo n.º 3
0
 public override ECFieldElement Square()
 {
     uint[] z = Nat256.Create();
     SecP256K1Field.Square(x, z);
     return(new SecP256K1FieldElement(z));
 }
Ejemplo n.º 4
0
        public override ECPoint Twice()
        {
            if (this.IsInfinity)
            {
                return(this);
            }

            ECCurve curve = this.Curve;

            SecP256K1FieldElement Y1 = (SecP256K1FieldElement)this.RawYCoord;

            if (Y1.IsZero)
            {
                return(curve.Infinity);
            }

            SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.RawXCoord, Z1 = (SecP256K1FieldElement)this.RawZCoords[0];

            uint c;

            uint[] Y1Squared = Nat256.Create();
            SecP256K1Field.Square(Y1.x, Y1Squared);

            uint[] T = Nat256.Create();
            SecP256K1Field.Square(Y1Squared, T);

            uint[] M = Nat256.Create();
            SecP256K1Field.Square(X1.x, M);
            c = Nat256.AddBothTo(M, M, M);
            SecP256K1Field.Reduce32(c, M);

            uint[] S = Y1Squared;
            SecP256K1Field.Multiply(Y1Squared, X1.x, S);
            c = Nat.ShiftUpBits(8, S, 2, 0);
            SecP256K1Field.Reduce32(c, S);

            uint[] t1 = Nat256.Create();
            c = Nat.ShiftUpBits(8, T, 3, 0, t1);
            SecP256K1Field.Reduce32(c, t1);

            SecP256K1FieldElement X3 = new SecP256K1FieldElement(T);

            SecP256K1Field.Square(M, X3.x);
            SecP256K1Field.Subtract(X3.x, S, X3.x);
            SecP256K1Field.Subtract(X3.x, S, X3.x);

            SecP256K1FieldElement Y3 = new SecP256K1FieldElement(S);

            SecP256K1Field.Subtract(S, X3.x, Y3.x);
            SecP256K1Field.Multiply(Y3.x, M, Y3.x);
            SecP256K1Field.Subtract(Y3.x, t1, Y3.x);

            SecP256K1FieldElement Z3 = new SecP256K1FieldElement(M);

            SecP256K1Field.Twice(Y1.x, Z3.x);
            if (!Z1.IsOne)
            {
                SecP256K1Field.Multiply(Z3.x, Z1.x, Z3.x);
            }

            return(new SecP256K1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed));
        }